Monodromy and Betti numbers of weighted complete intersections
type: Item
instance of: scholarly article
title: Monodromy and Betti numbers of weighted complete intersections
zbMATH Open document ID: 0595.32011
DOI: 10.1016/0040-9383(85)90009-6
published in: Topology
publication date: 1985-01-01T00:00:00Z
review text: Let (X,0) a weighted complete intersection of \(({\mathbb{C}}^ m,0)\), f: (X,0)\(\to ({\mathbb{C}},0)\) a holomorphic germ induced by a weighted homogeneous polynomial and \((X_ 0,0)=(f^{-1}(0),0)\). Assume that 0 is an isolated singularity of \((X_ 0,0)\), dim \(X_ 0\geq 1\). The aim of the paper is the investigation of the topology of \((X_ 0,0)\). More precisely, the monodromy operator associated to f is investigated extending results of Brieskorn, Hamm, Milnor and Orlik. Topological consequences are derived, e.g. the middle Betti number of the link of (X,0) is computed. Also the mixed Hodge structure of the Milnor fiber of (X,0) is computed (dim \(X\leq 3)\).
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 3957600
zbMATH Keywords: Gauss-Manin connection
zbMATH Keywords: weighted complete intersection
zbMATH Keywords: isolated singularity
zbMATH Keywords: monodromy operator
zbMATH Keywords: Betti number
zbMATH Keywords: mixed Hodge structure
author: Alexandru Dimca
MaRDI profile type: Publication
full work available at URL: 0040-9383(85)90009-6
OpenAlex ID: W1982852200
description: scientific article; zbMATH DE number 3957600